Instrument for dividing lengths according to the golden section.



P. NICOLE. INSTRUMENT FOR DIVIDING LENGTHS ACCORDING TO THE GOLDENSECTION APPLICATION FILED AUG.9. I9I7.

Patented June 4, 1918.

ltere were LAUSANNE; Swim-@Beesd l INSTRUMENT non mvlnmG LENGTITISAcconmn 'ro THE GOLDEN SECTION.

i ofsaajzenad, 'residing' a Lausanne, csaif A eis cette@ lenga ,of.lmez'folifming to@ #we e ,Cefedeeae @if en# Zelden@ -hevelmrentee@erwin `newfend ,use ful `lmprovenients inlnstruinents for D1- laeng'thsAccording" Golden Section 0f @cette toiletries e Speel@ Gatien. n y AThe Present Brennen relates t@ i en iestrnrnent` lfer jlvdividin'gfup,lengths Qr num here @meningite :the gelden secties, man 1 ing.it`possilole` ivithoit any Iignring,I and Strumenti, td 'eadi @Whew ,therelative values of a divisitm made Vaccording to. the

- golden"` section.

i The gc'il'denl Section is the wellp-lmoivn so` lutyio of the problemto divide line up inte two ulie'qel parte :S0 as t0 here the samerelation between the vvvholje line and its largersection, betvveentliislarger section and theV smaller,` or the relation" afterthe formula: p

ATB Ao Tee this' line "(Si 'Fie` lief "die @demeaning dmv/1115er i Will`have to be read on the line A' D or on" lovvs: :Bisect baser-'lineerect perpenl` deelar' B D," C1B @finalA inf length .t0 A`Bpdes'cribeian arcfv'vith radins' equal to lengthsfelgisht @edenSWekt-O" the" fermate given; "v

line A B is assuniedfto move parallel to itself', that ijs to say, `te'kepalways at right anglestefthe line B D and if azero point 1s kept onthis line;"thelength1 of Vthe lineLA B' yits eiitension. each differentpositionl of line A B, thetrianglfes "remaining simi-lar and the lille,C D remaining stationary, this line will divide the line A B in tWosections having the desired relationshiplfQn `one side t ere will be ashortersectiorr and on the other side a longer sectiornand both sectimeherein. at te@ lie .C D While the eter- 111- dividing, :fighe baselineAf-:Became Setting peint wie? the im@ B D5 Win indi! l cate jthe `lengthof:` the shorter section, and

mayibge `alecInpli-shed"with the instrument made according `to thepresent invention. p

`The'snistrnmfenty made according to this the `interefallfefiielitfivththe 111161K D, the length# the nager Seesen. `"an, this inventincomprises" a triangular device prothe 4projection being made paralleltothe smaller cathetus; thestraight edge is adapted to assume in thedevice positions parallel tothe larger cathetns, in all of whichpositions its zero points are on a transverse line Which dividesaccording to thegolden sec tion each right `line`parallel` to` thelarger cathetus,` and is limited by the scale line on tlieotherside `ofthev triangle lnamely` the hypotennse `and the 'smaller lcathetiis.

ln the dra'vvingz n Figure Itis a plan viefvv ofthe instrument made inaccordance with my invention.

Fig. 2 isa cross section on line. v -b Fig. G is a cross' section on theline k Fig. and i i Figf'isa cross section taken on the 1in@ Z-L-,mlF-gf1, i p This instrument jC0 n prisesa bottom plate shaped like aldraftsmanls triangle provided- Withscales on its three sides ashereinbefore descri-beil,- and a flat rule or straight edgeprovidedfvvith scales lon its tWofedges as `hereinleforedescribed; andfitted so as to slid'e andl Iferriain` parallely to the "base-line A B;The member invvhich Athe straight edge" slides is a transverse 'brace' lin the "bottom plate, andpthis brace is `located `in the dividingl-iliie@'-DfdividingA B accordingto the golden section.` Both bottom plate andthe searched for numbers may be read toasstraight edge may be made ofmetal or Wood or any suitable material, and provided with layers ofcelluloid at the parts carrying the scales. i l 4 i The scale on thebase-line A B or the larger cathetus is made in units and tenths ofunits with its zero point at B. The scale of the hypotenuse A D with itszero point at D, is al projection of the scale on larger cathetus AB,`this projection` being made parallel tothe smaller cathetus Bj D.`AThe scale on the smaller cathetus B D, has its zero vpoint at D and isdivided into units which are one half the length of the previous unitsand consequently of the same number fof units as the scales on thelarger cathetus and the hypotenuse. The scales onthe straight edge aresimilar and correspond to that on the `larger cathetus A B except thatAtheir zero points are located on the dividing line C D and the units ofboth these scales extend inl both directions from their zero points.

The brace of the bottom plate is provided with a groove 2, of Which thedividing line C D is the geometrical axis, and the straight edge has abutton 3 tted thereto and screwed to a slide 4 which is movable Withinsaid groove. The construction is such that When the slide l moves alongthe groove 2, the straight edge is always parallel to line A B and thezero points of its scales are always Vvertically above the dividing lineC D, or,

speaking from a geometrical standpoint, always coincide with thisdividing line. y The scale on the smaller cathetus on Which there mayalso'be read the zero points of the Whole numbers or lengths to bedivided up, useful for determining Whether the straight edge ismaintained parallel to the larger cathetus A B.

Owing to the arrangement of the scales the instrument When being usedmay be grasped With the left hand, While resting the instrument With thelarger cathetus upon a table or other support, so that the right handmay be employed to adjust the straight edge to the position in which oneof its edges coincides exactly With the number representing the lengthto be divided as `the same appears on the hypotenuse A D, the divisionsof the scale on the hypotenusey being somewhat larger than those of thescale on the larger cathetus, and hence the more easily read. At theintersecting points ofthe scales of the straight edge with the scale onthe hypotenuse, and the scale on thesmaller cathetus,

certain the: golden section. Thus for instance for the length250vread on`the hypotV enuse, the scale onthe straight edge indicates 154.5 and`95.5, and forthe length 216 "indicatesll and 82.' i i It is evidentthat the units of the scales 1. .Anins trument of the classF describedlcomprising a triangle, a brace connecting the base of the `trizmgle withthe opposite angle the axis of which brace divides thebase of thetriangle acc'rdingtothe golden" section, anda straight edge movableonsaid brace so as to assume at`allt1mes1apos1t1on parallel to the base ofthe triangle,'tl1`e saidfl triangle "andfstraight edge being provided ewith scales so that by` adiustingthe straight edge to position 'the'golden vsection of a, given dimension may be read'thereon. l

2. An instrument ofthe class described" comprising a rightangletriangle, a brace 4connecting the base ofthe "triangle With theopposite angle, Which brace has agroove` therein vvhilethe axisthereofdi'vides the base of a triangle according tothe golden section, aslide movable in the groove in the' said brace, and a straightedgesecured to' the said slide so as to assume at all times a positionparallel to the base of the :triangle the sides of the triangle and thelstraight edge being provided Withscales so that by" adjusting thestraight edge" toposition the golden section of a givenY dimension maybe read thereon. 1

3. An instrument of the class described comprising a right angledtriangle the smaller cathetus of vvhich 'is equal in length to one halfof the larger cathetus or side of the triangle used asa base, a braceconnect` ing thebase of the triangle vviththefopposite1 l angle, which'brace has a'l groove; thereinf While the axis thereof divides the@ larga1.

cathetus or base of the triangleaccording to the golden section, a slide'movable in the groove inthesaid brace, and a straight edge secured tothesad slide so astobe parallel at all ltimes tothe larger cathetus orbase'of the triangle, the larger cathetus ,or base of the triangle, thesmaller, cathetusL andthe of the same inumber oflesuitable ufnits,`fand"l10 hypotenuseeach being previded with a scale' the straight "edgevbeing provided `vvith af scale the zero point of vvhiclilies above theaxis of the said brace and extends in opposite directions therefrom, theunits in this scale being the same length as the unitsin the scale onthe larger cathetus or base of u Witnesses: l,

l EDW. EMMANUEL, y

, lW. y SNELL.

Copies of this patent may be obtained for ve cents eac-h14 byaddressiiig" the Gonndiasibner` orfalzimltsi.r n;

` Washington, 2D.. G.

